Oh. X
2J5
Appendix: DISOUSSIOK OF FIG. X.g, p. 221
To get from the experimental counting rates given by the left-hand scale
to the absolute production rates given by the right-hand one, the counter is
calibrated in a pile where "nv" is known ( "nV" is what we v.-ould call a flux
if we were dealing with a beam rather than with isotropic velocities). If
we regie ct the high^nergy collimated neutrons in the atmosphere (an assump-
tion which might be justified for x » 57 fifo*) w can then call the atmo-
spheric neutron velocities isotropic, so that the calibration is justified.
Once we know nV we can calculate the rate of neutron absorption per gram of
air, and we can certainly replace "abeorbed" by "produced" since there is an
equilibrium condition.
it might be heartening to point out that the order. pf magnitude of these
production rates can be predicted by elementary considerations, starting from
the proton intensity given in Fig. X.6, p. 222.
We shall have to make three arbitrary assumptions:
1, For x > 57 g/cm 2 the density of neutrons and protons is very roughly the
same. (At these depths moat nucleons are secondaries, and the number of
secondary neutrons and protons should not be too different.)
2 A neutron is "absorbed" as soon as it hits its first "air" nucleus-
5. It hits an air nucleus after travelling 57 &/cm 2 , i.e. after a distance
L = 57/^ am (fi is the density of air).
Also remember the assumptions of the calibration: a. Isotropic velocities,
b. Equilibrium.
V.'iih these assumptions the production rate = the collision rate 5 Rj
■v-V
-1 _=j X.20
collisions sec cm '?
where V is the average velocity, L is the mean free path.
All that remains is to state nV in terms of I ;
: , and this may be done
vert . '
almost immediately from the sketch. The number of
particles effusing normally through the unit-area
hole in the box is, by definition,
dK - I , dt dw
vert.
but, as discussed in every book on kinetic theory, it
should follow from the sketch that
i/V- Xji~>{it
dN
nV
tS dt 7^
4-7T
4tTI
'vert .
41TX
Thus X.20 becomes
■ ytrt .
-1 -*
collisions sec cm >
L S7 7?
However the croduction rate of Fig. X. 5 is expressed per gram rather than
per cm?, so our expression must still be divided by p. The -'« ™- ™*
we have
r -
4tT I vt ^t,
57
p ' s cancel, and
collisions sec * g
2 ?6 Appendix (continued.) Ch. X.
If £rm Fig. X.6, p. 222, we pick a value such as I v = rt = 5 x 10" 2 at
R 1 i — I'D"? at x: 400 §/»«
400, we find
Compariaon with Pig. X.J, p. 221, ahowo that the agreement, f ortuitoualy,
is quite good.
REFERENCES FOR COSMIC RAYS
1. Montgomery, D.J.X., "Cosmic Ray Physics," 1949
2. Janossy, L. , "Cosmic Rays," 1948
3. Rossi. D., "Interpretation of Cosmic Ray Phenomena,"
Rev, Mod. Phys. 20, 537 ('48).
4. Helsenberg, W,, "Cosmic Radiation," 1943
5. Cosmic Ray Symposium, Rev. Mod. Phys. 21, ('49)
6. Jauch, J.M., "Cosmic Rays," Tiucleoni cs 4, (Apr and May '49)
7. Tiomno and Wheeler, "Guide to the Literature of Elementary
Particle Physics, Including Cosmic Rays," American Scien-
tist 37 (Apr. and July '49) Also bound separately.
H. Papers delivered alt the International Conference on Cosmic
Rays, CnaaO) Italy; Sept. 1949 (to be published)
9. Symposium of the Inter university Cosmic Ray Laboratories,
Echo Lake, June 1949. (To be published early in 1950 by
the U.S. Government Printing Office.)
PROBLEMS
1, If you were travelling in an interplanetary space snip, what
sort of apparatus would you need to measure the total Inten-
sity of cosmic rays?
2. Assume that your laboratory is at tiie top of the atmosphere.
Design an experiment to set an upper limit on the intensity
of urimary electrons m cosmic rays.
3, Plot the semi-vertex angle of t'l
function of p at A = 50°.
g] Lowed
;ones
( K)
Some notes addsd Sap. 1950, and July I951
NOTES OK MESON TABLE, P. 153
237
neutral ^arMclL^ ** ^ lst °- Thar9 >W b«n reporta of charged and
"find But" f L^ flo 8; 5 w (i) .i^iS'v- L erhap : 220Qm ' Sea Rochse -
Anderson. Fhys Hev 78 2W f4l- » T t ' ^**' risia °' Oowan - Md
' y Be/ ' -gr',Z°^ 5 °J' Armenteros, Barker, Butler, Cachon, Emd
Chapman, Nature 167 . 501 ('51),
— S £ BV - ° ^» -LUj I pij. The maea of the n° is diacuaaed below.
, - ^»- -" 9V - g^ i m { Pl). The mean life of the v" ia dlacuesed below.
THE NEUTRAL tf-MSSON
4' 1 ',T r 3 l 51 >' and a r^Iew of experimentiper-fbrmad inside +fc«
vacuum tank, by Oardner et al . , Science HI . 191 (150). ^ th °
^ Next we Mention briefly three experiments which indicate the existence of
a -FT which decays into two gammas, probably in less than 10-13 sac.
*** V? Bt ' ■* haVS been obBerved *° c °oa from various targets when bombarded
with high-energy protons*. These A have a production crosa-section whoee
dependence upon proton energy i a much like that of charged pi on cross-sect Ions.
The ^-energy ia roughly 70 Mev on the average (half of the energy of a TT± )
ana their energy spread is in agreement with the floppier shift due to the ve
lOClLV Of* t.ho Tlfl rflrrr. maarvna t -P+ =>-- ^^n*,l„4 j. i_ . fJ . ~ , ,
locity of the parent me eons
fT"s "' '
Cou*,l
After examining the position of the shadow of
a lead screen (see the schematic sketch)
and calculating the distances traveled by
the n ! s before they decay (allowing for the
re lati viatic time dilatation}, the experi-
menters have been able to state that the
mean life of the ti° ' s is < 10"" sec. In
this time the pi on travels only a few mm.
-14
The upper limit on this mean life ha a been reduced to 5 X ISS"" <-.-. :j-.,
examining (indirectly) the point of origin of gammas produced by the decay of
n 8 produced ia coamic ray stars, observed in emulsions****. These gammas
create electron pair a, and the bisector of the angle between the two tracks
star ****** thS 9tar ' " lB fOWld t0 pasB V9r ^ c - loae t0 the
7n „ fMffC 1 , a ■ . ., In a second experiment, 7 ! s of about
I a i^T = MeV C?)) of nuclear origin ^ve been observed during the bom-
bardment of nuclei by 350 Mev x-rays from the Berkeley synchrotron**. Coinci-
dence and angular correlation meaaurementa show that these /' s are emitted in
pairs, moat probably from particles traveling with speeds up to about 0.3c,
This speed ia calculated" by considering the aberration of two 5" s emitted by
a relativxstic particle: aeen from the rest system of the emitter, the two
Photons must leave in opposite directions, but seen from the lab, they must
come off in a forward cone, ' '
Apparently the reaction is
/ + ft — v N 4 TT
where N stands for a Nucleon.
rr' mzli*$ % y
♦Bjorklund, Crandall, Moyer, and York, Phys. Rev. 77 . 21? ( l 50).
**3teinberger, Panofeky, and ataller, Fhya. Rev. 78. 802 ( l 50) ,
**!*» H asetumsd that th9 reader ha a already read the footnote, p,
"••Carlson, Hoopsr, and King, Phil. Mag. 41. 701 ("50)
221a
2?8
HEW DEVELOPMENTS
A a an example, suppose thai a J00 Mev photon is absorbed by a Maclean and
thai one Tr°of rest mass 135 Mev is created. Moreover, consider the special
case in the chq system where the pi on comes off forward, while the nude on
flies back. In this case the reader can easily check that in the lab the
nucleon has only about | Mev kinetic energy, leaving the pi on with kinetic
9nergy slighly greater than its rest mass. Now it is trivial to show that
a particle with KE = Mc 2 has a speed of 0.866c. Thus the /-emitters, deter-
mined by the aberration measurements to have speeds up to about 0.8c, are
probably TT*' s .
It has been shown* that an isolated IT with, spin ft or 1 cannot decay into
two /'a. Unless one wants to include the possibility cf spin t 1, it looks
as if a TT° has snin 0. Since the data seen to show a fair amount cf similarity
between charged and neutral oions, there may even be tentative indications thai-
all pious have spin 0.
13
A third experiment which indicates the mass of the 1T consists in allowing
ir"'s (made in the Berkeley cyclotron) to co.te to rest in a tank, of high-pressure
hydrogen**. We have already discussed on p. 13J the capture into Bohr orbit a
of mesons hy a nucleus. A pi on which is in a state of low angular momentum
will probably interact with the nucleus within the 10" J sec mean life cf the
oicn. In case the nucleus is nothing but a single proton, the result is not
a star, but probably one of the two following reactions
P-+fT** -* X(9 Mev) * f (1J2 Mev)
or P +■ Tf -* N(almost at rest) + tf (few Mev) 1
followed by it" -r 2-V (each of —65 Mev). '
Both cf these processes seem to occur.
The tr" 1 b are created inside the cyclotron where it is hard to run elec-
tronic counting equipment, so it has not been possible to determine the speed
of the IT* 'a by measuring the angular correlation of the coincident / ' s , but
one can still examine the Doppler effect, looking at the 7' s with a pair elec-
trometer***. 7rom this Doppler data it is claimed that 1.3 Mev < (M^ , - MjjoJ^ 1
< 4.7 Kev.
SCINTILLATION COUNTERS
It has not been mentioned in thie book that when charged particles (and
also- in particular- when 7" s) pass through many materials {solids, liquids,
and gases) these materials may give off visible light. The light may tnen
be detected with a photomultiplier tube. This is the principle cf the scintil-
lation counter, which is becoming of increasing Importance. These counters
can be made with pulse widths a a little as 10 ~9 aec, and have other characte-
ristic advantages: their response depends fairly linearly upon the energy
which the scintillator absorbs, so that they may be used ae spectrographs****,'
they are sensitive,- and a scintillating crystal does not have to be surrounded
with 3ome more or less transparent envelope, as do other counters.
For review articles see "Fluoreaeenceof Liquids under /-Bombardment^'
Kallman and Pu'rst, Nucleonics 7 . &9 (July 195°); ^ n< ^ a review by 3ell and
Jordan, Nucleonics . 5, ?0 (Oct. 194?).
*Yang, Fhys. Rev. 77 . 243 ( ' 50)
**Panofsky, Aamodt, and fork, Phvs. Rev . ~(9 , 825 ('50)
***i.e. one converts some of the gammas to pairs in a thin foil, measures the
total energy of the pair by determining the electron orbits in a magnetic field,
using counters in coincidence.
****Bell and Cassidy, Phys. Rev. 79 , 173 ('5°); Hofstader and Mclntyre, Phys.
Rev. 79, 369 ('50)
HEW DEVELOPMENTS 259
COSMIC RAYS: Fluctuations with Time
Diurnal Effect. For a discussion of this daily- variation in intensity
see Elllot an <i Do Iter, Pro_c. Roy. ggs. Lond A65, 157, ('JO).
Solar Effect. These variations follow solar activity (solar f ] areg
to L^T^^T' etC - } * Sae Forb « sh > Stinchcombe, and Schein, Phys. Rev.
19, 501 ('50); Adams, Phil. Mag. .. 4l_, 50* (' 5 0); Simpson, Phyft, Kevf$l, 895
GENERAL ^jMM MM Bgj TJTTCLEAE PFY.STnR
Bethe, HA. et al. "Wuclear Physics" Reveled. Fhys. 8, 82 (1956) 9 69
and 245 (1957). Referred to in this book as BotheT, B, and C. '
Bethe, H.A Elementary Nuclear Theory," Wiley, 1947; called Bethe D.
fermi, E. Elementary Particles , " Yale Fress, 1951.
Friach, 0. "Progress in Ivuclear Physics, 1" Academic Press, I950 .
Gamow, Gf. , and C. Critchfield "Theory of Atomic Wucleus and Wuclear Ener.v
bources, " Oxford, 19^9.
Goodman, C. "Science and Engineering of Wuclear Power;' Addison-tfesley 1947
Heitler, W. Quantum Theory of Radiatior" Oxford 1944 ...
LA 255 (AEGD 2664); Ferni, E. , "Houtr on Physics"
^^menta^'lSr'' ^ " (Matlonal EureaU ° f Standard), Superintendent of Docu-
Rasetti, E. "Elements of Nuclear Physios" Prentice -Ha 11 I936
Hosenfeld, L., "Wuclear Forces" Intsrscience 1948.
Schiff, L.I. "Quantum Mechanics" MaGraw-Kill 1949.
More specialised references are found at the end of the individual carters,
ana an the footnotes. '
The following bibliographies may also prove useful:
Beyer, R.T. "Foundations of Nuclear Physics" Dover 1949
Tiormc and Wheeler, "Guide to the Literature of Electa ry Particle Phvsics
Including Cosmic Rays" Am . Scientist . 57j 2C2 (1949); also bound' separately .
For biological applications, instruments, see
Siri, W.E. "Isotopic Tracers and Wuclear Radiations" McGraw-Hill 1949 (one of
the Hticlear Energy Series).
Note added Feb., Lggj
Some of the Sajor developments sir.ee the writing of these Hates ars
covered in the following books :
Marshall , 3 . S . "He 3 o n %s W MofiESW Kill, 1952
Thorndike, Ala- Mesons - A Sugary of Experimental Fact" McGraw Mill, 1<??2.
LePr knee Ringuet, L. "Cosmic Ra/s" Prentice-Hal"! , 15^0
Rossi, Bruno "High-Energy Particles" Prentice-Hall, 1052
S'J^tt ^•;'; rOSr93S ^ C °^ Raj P ^ 31CS " A ^ « the Co B eo-
nag en Confer ence*l Innersoience, 1952.
The ideas of cnarge- independence (isobopic spin) and fcheir apol^tio ns
to mesons and to light nuclei are discussed by M. Geil^ann and a HilSbrSd
m a for .nooning issue of the American Journal of Phys ics, " '
flgn M ^( ' lew developments are covered in tw, voltes of notes by R.P. Fevrma,
(l9:,l-,2) available from California Institute of Technology, Pasadena! ITIT.
Reference should also be made to a very complete new text dessrinfrts
Ui5±cs D J J - M - Slatu and >/.F. Weisskopf, Vfiley, 19^2.
240
DOTATION
The following list gives most o
that are quite standard are not list
special meaning in only one chapter,
it a symbol has a .meaning that needs
number following it gives the place
nition is found. Numerical values
f the symbols used. Symbols
ed. Where a symbol has a
the chapter number is stated.
fuller explanation, the page
in the text where the def i-
are on p . 240 .
ft- Bohr radius, 5.S9 x 10 cm
a a- Singlet ana triplet scatter-
* ing length, VI and IX
arrni Atomic mass unit, = Mj_
A Atomic mass number, N n Z
A Vector potential
b Collision parameter, 27 ,ZZS
BE Binding energy
D
e
E
e
f(0
i
%
i
x
i
;-.
".
Q
N
N
P
S
0.
Q
VI and IX, coeff. of tth
partial wave, 117
IX, thickness
electronic charge = -4.805
x lO' 1 " esu
, e e , etc., unit vectors
Energy eigenvalue, T + IT
Electric field strength,-?^
) Angular dependence of
wave
Total angular momentum of
atom, I + J
Coupling constant, Ecrmi
constant
h/2tT
Magnetic Eield
Total nuclear ang. momentum
Intensity, erg cm^sec " l
II, average ionization
potential, 30
Total ang. momentum of
extra-nuclear atom
Propagation constant, 2rr/2
Radiation length, 49
Mean free path for pair
production, 49
REST mass of electron
Rest mass of a particle
Index of refraction
a Neutron g
Atoms or nuclei per cm
II, electrons cnT 3 , 28
Magnetic ri&idity, (pc/2e)=#/>
,£) or q(r,rj, IX, slowing '
down density, 187
IX, rate of production of
neutrons 1 , 184
Energy of reaction, exo-
thermic
QUadrupole moment
Radius of electron and
of proton
X, radius of earth
Ry
s
S
T
U
IT
V
Vv'
x
7:
r
r
e
&
K
I
A
K
A
A
/*
r
or
<r(e)
<r
<r
*?
Radius of potential well.
Range
R3 r dberg energy, -13.52 ev
jspin angular momentum
Kinetic energy, half-lif e,
temperature .
Potential energy
Till i velocity
Velocity
Total relativistic energy, 5
Atmospheric depth, g can*, 215
Charge of particle in units
Of ^--electfoniG cViarge.
Charge of incident particle
II, h^/ic'' , energy parameter
VI 1> lPfi
VJ - J t,V ' ■ tJ
V/c
phase shift of -tth partial
wave ,
I - (t+) '*
X, angle between T and west,
2 25
Till, energy width of reso-
nance at f max. , 154
IX, In neutron energy
IX, neutron scattering angle
in lab . S7fstem, 182
Total scattering angle, 36
Range of meson field, 135
Mean free path, 184
Radioactive decay const, 1
X, magnetic latitude, 225
Cornpton wavelength/2-rr
IX, absorption mean free
path, 184
reduced mass
Nuclear magneton
Magnetic moment
V , hv/mc^
IX, reduction In In (neutron
energy) per collision, 183
Pauli spin operator, 112
Differential cross section
Total cross section
Klein-Nishina scattering
cross sectlon( Cornpton), 41
II, o~ for photoelectric
effect
II, Thomson cross section
141
% II, Thickness in g/em^
t Mean life
T£) IX, neutron "age"
to angular frequency, solid angle
fl Volume of nox for normalization
Denotes exeited nucleus
Order of magn:
Approximately
■
*** Order of magnitude
r
a = #% e 2
£42
TABLE OF PHYSICAL CONSTANTS
General Physical Constants :
0,529 x 10 ■ cm. Bohr Re din a
e^/yic «= 1/157-05 Fine structure constant
J?e £s l_
in
x 10 cm/sec. Velocity of light
x ip""*0 eau = 1.602 x 10" emu. Electronic charge
D~^" e cm^/sec . Fermi constant in "bets decay, p.
10 ' erg-sec. Planck constant
, x 10 ' erg-sec.
l.Jfl x lO - !" erg/degree. Boltzmann constant
6.025 x 10 5 /mole. Avogadro's number
2.82 x 10 * cm. Classical electron radius
c
oc =
c =
a =
g «6
h =
H =
k «a
2.988
4.805
2.5 x
6.624
1.054
'a
-li
^ = #/mc = 5.86 x 10~ iJ - cm. Compton wavelength/2'Tr'
Deutoron:
n-p scattering tf «= 20 , J
Triplet state t (p. 115)
BE = 2.25 Mev = 5.58 x 10
U, = -21.0 Mev, Veil depth
Tq = 2.82 x 10 -1 ? cm
barna
-6
erg
n-p triplet scattering C^=4.4 barna
a j = 0,59 x 10~ 12 cm
Wave fen phase at edge of well: 108
Singlet state: (p. 120)
U 1 = -11.5 Mev, Well depth
n-p singlet scattering a, = 68 barns
a,= -2.52 x 10~ 12 cm ,
Quadrupole moment Q,- D = 0.00275 x 10"
lP«
15)
Magnetic Moments;
■^Bohr = 0-9 2 7 5 x 10" 20 erg/gauss
/'nuclear -■ 5- oi * * 10 erg/gauss = l/185^ Bohr
/*electron = -1-002 >" BDhr
/"proton =^2.7896 >^ cIeGr
/"neutron — -l.ylOp yW nuc x ea r
/^deuteron~ ^*°5647yW nuc ^ eBr
Ma s se s :
(see p. 2; mass
formula, p. 7)
% -
Mp =
Ma-
m =
M ir +
1 amu = 1.660J x 10~^ 4 g = 951 Mev
1.00759 amu
1.00898 amu
1/18J7-561 M H = 9.1066 x 10 d ° g= 0.51
= l40.8 Mev = 276±6 electron masses
=158 Mav
= 107 ■ Mev
z
270 electron masses
210-4 electron masses
Nuclear Spins:
electron if
neutron i-
proton J
deute
triti
Li°
Li 7
Be 9
B !o
B 11
»ron 1
.um.H? jg
1
5/ 2
V 2
5
3/2
Mev. Maas of electron
243
Miscellaneous Constants, in Alphabet! cai Order;
Curie = J.71 x 1Q 10 disintegrations/as c
Dose (see p. 18)
e.v. = 1.6 ^ lCr iei erg
e.v. = 8100 etc -1 for photon
e.v. = 11,600° Aba. (setting 1 e.v. *= fcTJ
k. propagation constant for electron = \jlp ^ E . ,„ el ^s) s= c.5i*iO \l j)sE m ev)
k , pr o c a ga t i on c o net a at for pt'ot on = JSM)s/ k .E »« e»^l = 3- 1 2 * i », ('<E. m e.Y)
J" ^radiation length (p. 4?)
^ - 550 e iti NTF Air
_ 9.7 cm in aluminum
.517 of. in leas
9 a — mean free -ath for cair production (p. ^9)
L.. ■ = 57 g/'em 2 . Geometrical collision length for air nuclei (p. 220)
Usv = 1.601 x 10" 6 erg j,
R , = 1.5 x ICT 1 ? A 3 (p. 6)
r™ roentgen e that X-ray doss *hich, passing through STP air, leave a
' 83 ergs/g, or liberates 1 esu of positive ions per cn^
Rydberg: R = 1J-52 e.Y.- 3 Rhc
R = 109,737 cm" 1 , Rydberg constant for infinite mass
T (half-life, gaama decay, p. 96) „. . _
Velocity of thermal neutron = 2.7^ > 10^ cm/sec (thermal ss J00 Ahs.)^ ^
Velocity of thermal electron- 1 .117 x 10° cm/sec J £
x =1050 g/ra 2 , depth of standard atmosphere at sea level
Year = 3-16 * 10? secends
Athei
,-8
(thermal = 300° Abe.)
thermal neutron l'°l x J.U
^ =^1234o/electron volta) in Angst r oris, for photon
p: ±r = 1.225 xlO-3 g/cm 2
^Thcm^son^" 66 * 10 ~ 2 ^ „ . nQ ,s
X ( mean life; radioactive families, p. 17; ga^a aecay, p.ybj
J
INDEX
Abraham, M. , 4l , 44, 46, ?4
Absorption coeff iciente, 59
— th.iclcri.egs for cosmic rays, 220
Accelerator, betatron., 23
—Co ckroft-Wa.lt on, 24
— Cyclotron, 24
Adiabatic invar iance , 29
Allen, J. 3., 84
Allowed, regions (go ami rays), 227
— cones " " 229
Alpha-particles, Oh. Ill, 55-69
— lifetimes, 58
— long range, 6j
— 3emi -classical theory, 58
— 3peotra of. 66
— virtual level theory. 59
Alpha-alpha scattering, l49
Angular correlation, j»..-*> , 85
Angular momentum, total, 11
— electronic, 10
— nuclear, 10
— nuclear models, 169
— isomers, 106
— selection rules, 96
see also "spin 11 .
Anti-neutrino, 85, 86
Argonne graphite pile, 21J
Artificial production of if' s, 1%
Atmospheric data, 215
—depth, 215
Atomic mass, physical scale and
chemical scale, 2
— masa formula, 6
Auger electrons, 101, l4l
Avogadro's number, 2, 240
Axial vector, 99
BARRIERS, arbitrary, 56
— coulomb, 57) 58
— rectangular, 55
--factor in nuclear reactions, l42
163
Bartlett force, 112
Backs r, S, 4l, 44, 46, 54
Be , 149, energy diagram, 151
Eerkeley cyclotron
— deuteron beams, 177> 178
— neutron beams, 121
— jT- mesons, 131
Beta-decay, Oh. IV, 69-87
--theory, 72
--spectra, 76. 78
— rate, 76
— and gamma-decay, 89, 105
Betatron, 2J
Bethe, 8. , 257 , 30 , 31 , 32, p4
Beyer , 257 ■
Binding energy, J. 2
Block, $1
Bohr, 27, l48, 166
-- formula, 27
--orbits for ,> -me sons, 13J
Breit-wigner formula, 152, 157
Bremsatrahlung, 4j
Br S °, 106
Bursts, 219
C^ in atmosphere, 22Q
CAKEOH, gamma absorption resonance, 175
Cerenkov radiation, 32
Chadwick, J., 54, 54
Chain reactions, 208-215
Chemical binding effect on neutron
scattering, 194
Coherent scattering, 196-203
Cold neutrons, 180, 199, 203
Collision thickness in air, 22P
Commutation relations for I, 16
Compound nucleus, l47
Compton effect. 58, 40
— wavelength, 41 , 240
Conservation of energy, 69,
— in meson theory, 136
Constants, physical, 240
Conversion, internal, 101
Cu, gamma absorption resonance, 175
Coryell, 32
Uosmic Rays, Ch. X., 215-235
— absorption thickness, 22.o
— allowed cones, 229
— allowed regions, 227
— bursts. 219
— collision thickness, 22o
— east-west assymetry, 243
— electronic component, 2213,222
— forbidden regions, 257
— hard component, 221b
— intensity, 215, 222
— latitude effect, 235
— Liouville theorem, 2J2
— mesons in, 221,3,222
—motion of, in earth's field, 225
Jn sun 1 s field, 215
— N-component, 217, 222
— primary, 215, 233
— protons in primary radiation, 216.
— references, 237
— secondary radiation, 217, 22J
— shadow effect, 232
— showers, 49 219
— soft component, 221 jp 223
— stars, 217
— trajectory of, 225
Coulomb scattering, 125-127
Crane, H.R. , 84
Cross section for nuclear reactions,
141, 143
844
HB
Ccckroft-Walton accelerator, 24
Curie, 18, 240
Cyclotron, 23 (also sag Berkeley)
DECAY CONSTANT, A , 1
£ -functions, 106 ; rays , 2i9
Density of nuclear levels, 158, 161
Density of states in a box, ~J6
Detailed balance, 145
Deuteron, 113-121, 169
— nuclear potential, 115, 116
—stripping, 177
— virtual state, 120, 121, 175, 199
— wave function, 115-116
Diffraction of neutrons, 200-201
Diffusion theory (neutrons), 187-194
— length (neutrons), 1J>J
Dipole (aee Electric, Magnetic ...)
Dirac theory of the electron, 48
Disintegration of jy' a, jn 1 s, 152,22-1 a
Double j3 -decay, 86
EAST -WEST ASSYKETRY, 233
Einstein mase energy relation, 2
Elastic scattering of neutrona
181 -18?
Electric Dipole, 92
— abaorption at high energy, 100
— emission, 94. 96, 106
— static moment forbidden, 15
— radiation forbidden, 99
Electric quadrupole, 93
— emission, 100, 108
Electrons, existence in nucleus, 75
— negative energy, 71
Electronic component of cosmic
rays, 22U, 222
Ellis, J4, 54
Endothermic reactions, l4l, l44
Energy- diagrams, beta decay, 70
— Be° (compound nucleus), 151
— isomeric states, 106
Entropy of nucleus, l6l
Equilibrium, radioactive, secular,
17
Evaporation from nucleus, 162
Exchange forces
— experimental evidence, 121-123,178
— mesons, lj4
— saturation, 113
— types, 112
Exothermic reactions, l4l, 144
FEATHER rule, 32
Fermi, g . , ionization lose, 32
paper on pile theory,
208-213
Fermi age equation, 187-188
Fireman, 87
Fission, 164-208
— asymmetry in, I65
— in chain reactions, 208
— delayed neutrons, I67
— fragments, 166, 167
— neutrons emitted, I67
— stability against, 164
— triple, 167
Forbidden cones and regions, 228
— transitions, 100
— strictly forbidden transitions, 104
Form factor, 200-201
Fourier analysis of J, 107-109
F?r Tables, 82
Fur ry, 87
GAMMA RADIATION, Ch. V,, 89-106
— energy of, 89
—half-life, 96
— multipole expansion, 92
Gamcw , G. , 55
Gamow-Teller selection rule, 81
Gamow factor , 58
Gas model of nucleus, 159
Geometric nuclear a- , 22.0
Geiger-Nuttall law, 66
Glendenin, 32
"Golden Rule # l n 136, 148
"Golden Rule # 2" 142
G-oldberger, 177
Goldhaber, 175
Goodman , 237
Graphite filters, 203
Greisen, K. , 36, 4p, 54
Gyro magnetic ratio, anomalous, 20
HALF LIFE, defined, 1
— alpha radiation, 58
— beta " , 82
— gamma " , ^6
Hamilton, &5
Hard component of cosmic raya, 221b, 22.2
Hayakawa, 221
Heat of condensation, 4
— of condensation, 7
Heisenberg, W,, I37
—force, 112
Heitler,240 , 39, 4i , 45, 47, 48, 50, 54
He X 169
He 5, 169
High-energy scattering 121, 122
Hydrogen, ortho- and/para-, 199-200
H 5 , 169
Index of refraction for neutrona, 201-202
In 11 ?, 106
Induced emiasion, 95
Induction, nuclear magnetic, 15
Inghram, 87
Internal conversion, 101-105
— coefficient, 101 103
245
Internal conversion (cont.)
— experimental, 104-105
— relativistic treatment, 104
— selection rules, 104, 105
— theory, 101
Intensity of primary cosmic rays,21C
" ' ■ secondary " " ,222
Inverse processes, l45
11 , beta-decay, 85
Ionization of a gas, 33
— chamber, 33
— loss by heavy particles, 27
— electrons, JO
— — mesons
Isobar, defined, 1
— behavior of, 8
— stability of, 71
Isomerism, 106
Isotone, defined, 1
jamossy, 257, 57, 53, 5^, i?7
K-CAPTURE, 70, 71, 84
K-conversion, 101
Kennard, B.H., kl
Klein-Gordon equation, 134
Klein-Niehina formula, 4l
— plotted, 42
Konopinski, 81
Korff, S.A., 53
Kurie plot, 80
LA 24 and 255 , 237
Lagrangian, relatlvistic electro-
dynamic, 226
Larmor's theorem, 15
Latitude effect, 233
Lattes, 131
Lead, absorption of photons in, ^0
Lifetimes (see Half Lives)
Lindsay, 55, 37
Liquid Drop model, y
— applied to fission, 164
Li 6 , 170
Livingston, M.S., 237, 31 , 54
Low energy scattering, 194-195
— cross section, 119 , 120
MAGIC NUMBERS, 170
Magnetic Dipole, defined, 93
—emission, 95, 100, 109
Magnetic Moment, nuclaons, 13
— deutaron, 13, 171
——earth, 228
~3Un, 215
Magnetic rigidity, 225
Magneton, Bohr and Ku clear, 1J
Majorana, 86
—force, 112
Mass (amu) , 2
Maes, atosic mass formula, 6
— defect, 2
— number, 2
— reduced, 5
— relativistic, 4
— of mesons, 153
Matrix element, in beta-decay, 75, 81
— in gamma-decay, 92-96
Mattauch, 257
Mayer, M. 3. , 87
Mean free path for neutrons, 185-6, 189 32!
Mean life (Half life)
Meson, decay of tT and p, 132
— heavy, 135
— in cosmic rays, 220
— Tfand u, p and <r, 151-2
—neutral, 155, 221
— pseudo-scalar, vector, tensor, 135
—theory, 1% 23, 135-7
Minimum ionization, 131, 3 3
Mirror elements, 83
Mn, (n,n.) resonance, I56
Model, liquid drop, 5
— orbit, I67
— statistical gas, 159
Moment (see Magnetic, Electric, etc.)
Morrish, 84
Mott, 50
p-Jfeson, 151, 230, 223 (muon)
Multipole expansion, 92
N-QOMP0NENT, 21? , 222
Negative energy levels, 48
Neutral meson, 1J1, 221b
Neutrino, 69, 84-7
— antineutrino, 85
— flux from 3un, 85
—mass of, 79, 84
—virtual , 87
Neutron, age equation, 187-8
— beams from Berkeley cyclotron, 122
— capture in light nuclei, 174
—crystalline diffraction, 200-202
— decay of, 70
— density in atmosphere, 220
— diffusion theory, 187-94
— elastic scattering, 181 -85
— graphite filter, 203
— in cosmic rays, 22o
— index of refraction, 201-2
— interference cf, 196-205
— macrocrystalline scattering, 205
— nascent, 191
— neutron-neutron forces, 129
— neutron-proton forces, 113-23-
potentials, 122-3
scattering, 117-20
— polarization, 204-07
— ecattering in ortho-andpara-hy-irosen,
199-200
— slowing down, 181— S3
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Neutron sources, 179-81
—thermal, 4, 191-4
Notation defined
Nuclear forces, Ch. VI, 111-29
— non-central , 115-4
— spin- dependent , 114-5
Nuclear reactions, l44-5
— listed individually under Reactions
Nuclear shells, 150, 167,
ORBIT model of nucleus, 150, 16?
PACKING fraction, 2
Pair formation, 58, 47, 54
— in electric field, 73
— mean free path for, 4-9
Paneth, 64
Parent -daughter activity, 25
Parity in beta decay, 61
— gamma decay, 96-9
--compound nucleus, 149-52
Partial wave theory, 117-20, 194-5
Pauli, 157
— principle ; proton-proton scattering,
125'
— saturation of nuclear forces, 112
Penetration of nucleus ill internal
conversion, 104
Periodic shell structure, 9
Persistence of velocity, 186-8
Photodis integration of deuteron, 175
Photoelectric absorption, J8
Photonucler reactions, 175
Physical Constants, 240
-fT -meson, 131 , 22ia (pion)
Piles, chain-reacting theory by
Fermi, 208-13
— neutron yield, 180-1
— thermal column, 193-4
Planck radiation law, 94
Plane wave in polar eigenfunctiona ,
172
Polar vectors, 99
Polarization of Neutrons, 204-07
Polynomials, Legendre, 15
ponieranchuk, 224-
Positron, 48, 5^
— emission, 70-72
Powell, 151
Poynting vector, 89
Primakof, 137
Primary cosmic radiation, 215
— charge of, 233
Protons in cosmic rays, 215, 2.2Z
— proton forces, 123-28
— potential, 128
— scattering results, 128
QUADRUPOLE Moment, 15, 21
V, 89-106
RADUTION, Ch.
—length, 47
Radiative capture, n by M, 171
Radioactivity, 17
— geological aspects, 19
— biological effect j 18
Ra-Bs source, 179, 191
Radius of nucleus, 6^
Range of oc's, electrons, Jl-2
— of .cosmic ray particles , 222
Rarita, 12J
Kasetti, 257, T 101
Reactions; 6* -* \A ' — e.
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In («, T) resonance,
149
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179
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Silver (*,?-") re;., [47
Recoil experiment, &4
Rectangular barrier, 55
References, 237
Resonance, nuclear, l45
, theory, 152-157
— — , experimental data, 157 - 59
— absorption of dipole radiation, 100
p -Meson, 131
Richtmeyer, 4l
Roentgen arid rep, 18
Rosenfeld, L. , 237
Rossi, 36, 49, 54, 2l6, 222
Rutherford, E. , 34, 54
SATURATION of nuclear forces, 111-2
Scattering angle for electrons, 37
— Gompton, 40-2
— cosmic ray electrons, 55
—Coulomb, 34-6, 125-7
—of neutrons, 181 -5, I87, 194, 195
in crystals, 196-205
— partial wave theory, 117-20
— Thomson, 40
Scattering cross section, 118-20
— low-energy, 119-20
— high-energy, 121-2
Scattering length, Iy4-20I
Schiff, 237
Schein, ^l^, > 2lS, 2Z2, 233
847
A
SS^— ■
Sclwinger, 123, 199 W-igner elements, 83 |
Secondary cosmic radiation, 217, 22J Width, T , decay of compound nucleus, 1^
cosmic rays, 217,
98
Secular equilibrium, 17
Segre chart, 1
Segre and helmholz, &9
Selection rules, 96-100
— beta decay, 60
— Garaow-Teller, 81-2
Semi-empirical atomic mass, 6
Shadow effect, 2J2
Shell structure of nuclei, 9,
Sherwin, B4
Showers, 49 , 21&-2I3
Simpson, J. A., Jr. 211
Snyder, 1J1
Soft component of
221, 22?
Spectra, band, 11
— hyperfine, 10
Spherical harmonics, 97
Spin, dipole radiation.
— eigenf unctions, 123~5
—flip, 1?6~8
— inherent, 9-10
—multiplicity, 142, 1%
— nuclear, 74
— operator, 173
— see also Angular Momentum
Spontaneous emission, 89-94
— of two Quanta. 105
■ Stars, 1J1, 162, 175, 2 17
State function, molecular, 12
Statistics, 12
— of nuclei, 73
Stem-Geriach, 12
Stormer, 226
Stratton, J .n. , 44
Sun's magnetic field, 215
Symmetry and parity, 15°
Synchro- cyclotron, 24
rv, ry . 154, 15a
Williams, E.J., 36
X-radiation, 101
YUKAWA, 131, 134, 157-
167
ZEEMAN effect in Solar spectrum, 21 5
T AWT ALUM, y-ansorption res., 175
Teller, 175, 199, '33
Thomas-Fermi atom model, 57
Thomson cross section, 40
Thermal column, ] 9S-4
Thermal neutrona, 191^4, 20 5
Threshold , photodisintegration, 4
— reverse, 5
for nuclear reactions. l4l
Tiomno and Wheeler, 237
Two-quantum emission, 105
UNCERTAINTY principle, 148, 155, 13&
VALLARTA, 232
Virtual state of deuteron,
120
WENTZEL, 137
WK3 method, 62
Wheeler, 166, J33
248